Among top apps of 2011: Instagram, Dropbox, Onavo

For Christmas, millions of people found a smart phone under their tree: More than 6.8 million Android and Apple devices were activated, according to the market research firm Flurry.

The first thing those users did after powering up their phones: download applications. On Christmas Day alone, 242 million apps were downloaded, Flurry said.

With hundreds of thousands of apps available, it can be hard to know where to start. Here’s a guide to some that we can’t live without, with a bias toward those built in the Bay Area.

Instagram: San Francisco’s Instagram gained more than 15 million users in its first year by making it fun, fast and easy to share photos with friends and family. But it also solved a real problem: helping novice photographers take decent shots with their smart-phone cameras. The variety of attractive photo filters Instagram offers lets users improve their images with the tap of a finger. An update to the iOS app this year made the filters 200 times faster than before; an Android version is on its way. (iOS; free.)

Dropbox: Moving files around used to be hard. In 2007, Dropbox made it easy. You install the program anywhere – your phone, your MacBook, your PC at work – and it creates a magic folder backed up to the cloud. Add anything to the folder, and the changes show up almost instantly everywhere else. It’s a simple idea, but no one had gotten it right before Dropbox. The San Francisco startup had a monster year in 2011, shooting to upward of 50 million users while creating redesigned versions of its Android app and mobile website. (Most platforms; free, with paid options for more storage.)

Chase: The fact that this app lets you deposit a check by taking a picture of it with your Android phone, iPhone or iPad gave us all one less reason to occupy the banking system. Chase is the biggest bank to enable deposits via phone, but at least eight other banks and credit unions have apps with that feature, including Charles Schwab, USAA and State Farm Bank. (Android and iOS; free.)

Evernote: The tagline of this Mountain View startup makes a big promise: “Remember Everything.” But Evernote will help you get closer to that goal than any other app. Create notes of any kind – to-do lists, recipes, photos of where you parked your car – or store important files for safekeeping. A single search will retrieve any of them almost instantly, sparing your brain from having to remember the details. This year, Evernote released updates to its excellent apps for every major desktop and mobile platform, and also made its first acquisition: Skitch, another great app that helps people annotate images. (Most platforms; free, with paid options for extra features.)

CardMunch: One of those magical apps that makes you feel like you’re living in the future. Take a picture of a business card, upload it to the cloud, and in seconds it is transcribed and the contact information is sent to your phone. LinkedIn bought the company in January and made the service free (iOS; free.)

Tweetbot: The poorly received redesign of Twitter’s iPhone app this year sent thousands of tweeters into the loving embrace of Tweetbot, which bills itself as a Twitter app “with personality.” Indeed, the app is filled with lovely touches: configurable buttons, useful new gestures, and pixel-perfect design. (iOS; $2.99.)

Uber: Anyone who has hurled himself into traffic trying to score a cab in this taxi-bereft town will appreciate the five-star service offered by San Francisco’s Uber, which sends elegant town cars to your location quickly and at the tap of a finger. Your credit card is already on file with Uber, so there’s no need to carry cash. The top-notch service comes at a high price – a recent journey of barely a mile cost me $18 – but for a growing number of urbanites, Uber is a worthwhile indulgence. (iOS and Android; free.)

Pocket MUNI: If you struggle with navigating San Francisco’s bus system (ahem) you’ll do well to pick up one of the apps designed to make it a bit easier. I use Pocket MUNI, which improves on the free NextMuni.com site by allowing you to locate nearby stops, see a stop’s location relative to yours, and create lists of favorite stops for easy lookup. An update this year made Pocket MUNI a native iPad app as well, and it looks great on the bigger screen. (iOS; 99 cents.)

Rdio: Spotify gets all the love these days, but it’s worth mentioning the high quality of the mobile apps from its Silicon Valley competitor, Rdio. Slick apps for most major platforms let paid users sync as much music as their phones and tablets can hold for offline listening, while doing a better job than anyone at delivering recommendations for what else to check out. Rdio was also the first streaming music service to develop a native iPad app, and it’s gorgeous. (iOS, Android and Windows Phone 7; $9.99 a month.)

Onavo: Anyone struggling to stay under a bandwidth cap will want to check out Onavo, a free service that reduces the amount of data used by your favorite apps. Onavo compresses the data used by your apps without noticeably slowing them down. It will save you megabytes by the hundreds. (iOS and Android; free.)

Lookout Mobile Security: The rise of malware directed at mobile phones has created the need for software like Lookout’s, which does a great job identifying threats posed by innocuous-looking apps in the Android market that turn out to be malicious. It also backs up your data to the cloud and helps you find any device that goes missing. A paid version alerts you when you accidentally visit a malicious website and lets you remotely erase your phone if it goes missing. The company also introduced a free iOS version this year with features of its own. (Android and iOS; free and paid.)